University of Minnesota Combinatorics Seminar: 2020-2021

Date: 11/20/2020

Speaker: Eric Stucky

Strange Expectations for Simultaneous Cores
"b-cores" are a class of partitions that originally arose in the modular representation theory of the symmetric group; partitions that are simultaneously a- and b-cores are called (a,b)-cores. We discuss a Coxeter formulation of (a,b)-cores due to Williams and Thiel that allows us to define "(W,b)-cores" for any Weyl group W, as well as a quadratic form size that in type A counts the number of boxes in the Young diagram. In their original paper they used Ehrhart theory, as well as the "strange formula" of Freudenthal and de Vries, to compute the expected size of a (W,b)-core for simply-laced W. This talk is based on recent work with Williams and Thiel that reinterprets the story from their original paper somewhat to extend their results to all Weyl groups.

Strange Expectations for Simultaneous Cores

"b-cores" are a class of partitions that originally arose in the modular representation theory of the symmetric group; partitions that are simultaneously a- and b-cores are called (a,b)-cores. We discuss a Coxeter formulation of (a,b)-cores due to Williams and Thiel that allows us to define "(W,b)-cores" for any Weyl group W, as well as a quadratic form size that in type A counts the number of boxes in the Young diagram. In their original paper they used Ehrhart theory, as well as the "strange formula" of Freudenthal and de Vries, to compute the expected size of a (W,b)-core for simply-laced W. This talk is based on recent work with Williams and Thiel that reinterprets the story from their original paper somewhat to extend their results to all Weyl groups.